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The ATP Cup will see 24 nations split into six groups across three Australian cities, with eight teams emerging from the round-robin to compete in a knockout phase until one country is left standing.
Nadal had to twice fight back from a break down against the Japanese world number 72 in the opening set before winning the tiebreaker.
Men's title-holder Novak Djokovic eased into the last 16 but elsewhere there were surprises all over Melbourne Park with Williams the biggest victim and Federer fighting back from 4-8 down in a fifth-set tie-break with John Millman.
It was the 50th act of one of the greatest rivalries of the sport and the odds were heavily stacked against Federer as the Swiss had not beaten the Serb at a major since 2012 on the grass courts of Wimbledon.
The world number two blasted the top-ranked Spaniard off court 6-2, 7-6 (7/4) after world number 10 Roberto Bautista Agut caned Serbia's Dusan Lajovic 7-5, 6-1 in the other singles.
Meanwhile, world No. 1 Novak Djokovic headlines the initial men's singles entry list for the US Open, the organisers have announced.
Federer will not be at Flushing Meadows this year after he took the year off to recover from a knee surgery while defending champion Rafael Nadal joined a number of top seeds in refusing to travel to the US due to COVID-19 concerns.
The 17-time Grand Slam winner fended off Raonic's mighty serve to extend his 2020 winning run to 23-0, clinching his 80th career title and equalling Rafael Nadal's record of 35 Masters 1000 wins.
His decision will come as good news for the US Open organisers after several high-profile players, including former winners Rafael Nadal and Stan Wawrinka, pulled out over issues related to the novel coronavirus pandemic.
World No. 2 Rafael Nadal easily defeated unseeded Taylor Fritz 6-3, 6-2, in the final.
Results 231-240 of 281
